Question

In: Statistics and Probability

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final...

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the

null hypothesis, and final conclusion that addresses both the claim and the significance level

alpha. Use the P-value method.

A sample of 17 jellybeans with a mean weight of 0.8295 g was taken. Assume that

σ is known to be 0.0565 g. Consider a hypothesis test that uses a 0.05 significance level

to test the claim that the mean weight of all jellybeans is equal to 0.8550 g (the weight

necessary so that bags of jellybeans have the weight printed on the package). Assume

the weight is normally distributed.

Solutions

Expert Solution

Solution:

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 0.8550

Ha: 0.8550

The test statistics,

Z =( - )/ (/n)

= ( 0.8295 - 0.8550 ) / ( 0.0565 / 17 )

= -1.86

P-value =2* P(Z < z )

= 2 * P(Z < -1.86 )

= 2 * 0.0314

= 0.0628

The p-value is p = 0.0628, and since p = 0.0628 > 0.05, it is concluded that the null hypothesis is fail to rejected.

There is not enough evidence to test the claim that the mean weight of all jellybeans is equal to 0.8550 g

orchestra answered 2 years ago
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